The invention generally relates to the field of computer programs and systems, and specifically to the field of computer aided design (CAD), computer-aided engineering (CAE), modeling, and simulation.
A number of systems and programs are offered on the market for the design of parts or assemblies of parts. These so called CAD systems allow a user to construct and manipulate complex three-dimensional models of objects or assemblies of objects. CAD systems thus provide a representation of modeled objects using edges or lines, in certain cases with faces. Lines, edges, faces, or polygons may be represented in various manners, e.g., non-uniform rational basis-splines (NURBS).
These CAD systems manage parts or assemblies of parts of modeled objects, which are mainly specifications of geometry. In particular, CAD files contain specifications, from which geometry is generated. From geometry, a representation is generated. Specifications, geometry, and representations may be stored in a single CAD file or multiple CAD files. CAD systems include graphic tools for representing the modeled objects to the designers; these tools are dedicated to the display of complex objects—the typical size of the file representing an object in a CAD system ranges, but is typically on the megabyte order of magnitude for a part. An assembly may contain thousands of parts, and an assembly file is correspondingly large. A CAD system manages models of objects, which are stored in electronic files.
The advent of CAD and CAE systems allows for a wide range of representation possibilities for objects. One such representation is a finite element analysis (FEA) model. The terms FEA model, finite element (FE) model, finite element mesh, and mesh are used interchangeably throughout this application. A FE model typically represents a CAD model, and thus, may represent one or more parts or an entire assembly. A FE model is a system of points called nodes which are interconnected to make a grid, referred to as a mesh. The FE model may be programmed in such a way that the FE model has the properties of the underlying object or objects that it represents. When a FE model is programmed in such a way, it may be used to perform simulations of the object that it represents. For example, a FE model may be used to represent the interior cavity of a vehicle, the acoustic fluid surrounding a structure, and any number of real-world objects, including medical devices such as stents. When a given FE model represents an object and is programmed accordingly it may be used to simulate the real-world object itself. For example, a FE model representing a stent may be used to simulate the use of the stent in a real-life medical setting.
The usefulness of a finite element simulation however is limited by the accuracy of the simulation itself. For example, a common error in finite element simulations is a penetration, i.e., the simulation generating a result indicating that a surface of a FE model has been breached, or has breached a surface of another FE model, or a false gap between two surfaces that are in contact. While there are existing solutions to compensate for these errors, and enhance the accuracy of the finite element simulation, the existing solutions are inadequate.
Finite element simulations often involve contact between curved surfaces. A successful finite element simulation of the contact between curved surfaces typically relies on good resolution of these interfaces. However, faceted representations of surfaces based on exposed sides of finite elements are often not highly representative of the true geometry. This frequently results in various difficulties in robustly getting a simulation started and often causes significant inaccuracy to solution results of interest.
Two methods exist in the art to handle these errors. One is known as the Isogeometric Finite Element method, in which the finite element formulation is directly based on CAD-type spatial interpolation (NURBS, etc.). Professor Thomas J. R. Hughes has been a lead researcher and proponent of this approach. Some form of this approach has been adopted in LS-Dyna® and perhaps other CAD Systems.
Another known method for handling these errors is through circumferential and spherical smoothing capability. With this capability, the user indicates the approximate cylindrical axis for circumferential smoothing or the approximate spherical center for spherical smoothing. If the CAD geometry is known the process will automatically write the cylindrical axis or spherical center for portions of finite element based surfaces whose associated CAD geometry is precisely axisymmetric or spherical, respectively. This method introduces corrections to penetration/gap distance calculations based on differences between initial CAD and finite-element representations of a given surface.
Disadvantages of the Isogeometric Finite Element method include a high level of connectivity resulting in quite a full population of a stiffness matrix. Also a higher-order of continuity of interpolators can be disadvantageous for some types of deformation modes. Further, the method is non-intuitive (for example control points are not on the true surface).
Drawbacks and limitations of the circumferential/spherical smoothing method include the tediousness of operation for users to specify the cylindrical axes or spherical center in some cases. Further, this method is only applicable to certain surface shapes.